If axb=cxdand axc=bxd,show that a−dis parallel to b−c,where a=dand b=⋅
Show that the points A, B and C with position vectors, a=3i^−4j^−4k^, b=2i^−j^+k^and c=i^−3j^−5k^ respectively form the vertices of a right angled triangle.
The two adjacent sides of a parallelogram are 2i^−4j^+5k^and i^−2j^−3k^. Find the unit vector parallel to its diagonal. Also, find its area.
If either a=0or b=0, then a⋅b=0But the converse need not be true. Justify your answer with an example.